Every year natural disasters cause damages running into the billions of dollars. A mathematical theory that would help explain, predict, and even avert these fateful phenomena would certainly go a long way in allaying our fears and reducing damages. Such a theory was, in fact, developed some 30 years ago. Unfortunately, it did not live up to the expectations that had been placed in it. So-called catastrophe theory experienced its short yet brilliant rise to fame in the 1970s and 1980s, shortly before disappearing with hardly a trace. The theory nevertheless deserves to be taken seriously. It not only deals with disasters in the conventional sense of the word but shows how sudden and abrupt changes in nature may occur even though the underlying parameters are being varied only gradually.

Phenomena related to catastrophe theory can easily be observed in daily life. Take, for example, a kettle of water on the kitchen stove that is slowly heating up. The water starts to bubble with increasing intensity, until suddenly—at precisely 100 degrees Celsius—something quite different happens: It starts to boil. The water becomes gaseous, that is, it starts to evaporate—an effect known in physics as a change of state.

Another area in which catastrophe theory can be applied is the stability of structures. The more weight that is loaded on to a bridge, the more it suffers a certain amount of deformation. The changes are usually barely perceptible. But at a certain point, disaster strikes: The bridge collapses. For these and other catastrophes only very few variables are responsible. Over vast ranges of values, changes in these so-called control variables do not entail any observable reaction. But as soon as one of them moves ever so slightly beyond the critical point,

the catastrophe occurs. It is the straw that breaks the camel’s back.

Catastrophe theory was developed by the French scientist René Thom, who died on October 25, 2002. Born in 1923 in Montbéliard in eastern France, he spent the first few years of the Second World War with his brother in safety in Switzerland before returning to France. In Paris he attended Ecole Normale Supérieure, an elite college for the very best students, from 1943 to 1946. He was hardly an eminent mathematician at the time. It was only on his second attempt that he managed to pass the grueling entrance exam to Normale Sup. But not long thereafter Thom wrote a brilliant doctoral thesis for which he received in 1958 the most significant award a mathematician can get, the Fields Medal.

Some years later Thom succeeded in proving a surprising theorem. He was attempting to classify “discontinuities” and discovered, to his utter surprise, that such breaks in continuity could be classified into a mere seven categories. This astonishing result showed that a whole variety of natural phenomena could be reduced to a mere handful of scenarios.

Thom called the discontinuities “catastrophes” and—as every public relations professional knows—the name is everything. Henceforth catastrophe theory was in everyone’s mouth. Unfortunately, at some point, Thom’s theory fell into the wrong hands. His main book on the subject—quite incomprehensible to the layman—became a best-seller that many people were quite happy to put on their bookshelves without ever having opened it.

Then the members of other disciplines started to take notice. True, Thom himself suspected that the results of his research could be applied to disciplines other than physics. But when social scientists and other representatives of the “soft” sciences, who normally do not work quantitatively, started to become interested in Thom’s new theory, there was no turning back.

The respectability of catastrophe theory was irretrievably lost. All of a sudden and at every turn people thought that they detected Thom’s catastrophes. Psychologists di-

agnosed them in the sudden irate outbursts of choleric patients, linguists detected them in sound shifts, behavioral scientists saw them in the aggressive behavior of dogs, financial analysts detected them in stock market crashes. Sociologists interpreted prison revolts and strikes as Thom catastrophes, whereas historians thought that revolutions fell into that category and traffic engineers believed the same to be true for traffic jams. Even Salvador Dali was inspired by catastrophe theory for one of his paintings.

At the beginning mathematicians were delighted by the fact that at long last their discipline was being recognized by colleagues in other fields. But it did not end well. Experts, or at least those who thought of themselves as such, believed they could predict the exact timing of such discontinuities. The ability of foretelling the precise moment of the next stock market crash or the time of the next outbreak of civil war would, they thought, only be a matter of time. But matters had gone too far. In 1978 the mathematicians Hector Sussmann and Raphael Zahler published a devastating critique in the philosophical periodical Synthèse. They attacked the failed attempts of those who sought to apply catastrophe theory to social and biological phenomena. They argued that the mathematical theory only had a right to exist in the fields of physics and engineering.

Then one day the theory was gone. It had disappeared from the scholarly literature, just as suddenly as the catastrophes it claimed to analyze. Maybe it would have been better had the theory not become so popular and if it had, instead, oriented itself along the doctrines of the Kabbalah, the esoteric teachings of Judaism. Since Kabbala is a secret and mystical school of thought, its teachings may only be transmitted to mature men, so that over-zealous laypeople would not be able to wreak havoc with it. Such an approach would have surely been of benefit to catastrophe theory.